THE PROPERTIES OF NEW APPROACH OF FRACTIONAL ORDER DERIVATIVE


KARCI A.

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY, cilt.30, ss.487-501, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30 Konu: 3
  • Basım Tarihi: 2015
  • Dergi Adı: JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY
  • Sayfa Sayıları: ss.487-501

Özet

Derivative concept has got about 300-years history. The fractional order derivative concept also has got a long-term history and there are many studies on this concept. The reason for these studies is the belief of better modelling the physical systems with fractional order derivative; the classical derivative is beneficial to model the physical systems locally and the fractional order derivative is beneficial to model physical systems globally. However, the fractional order derivative methods in literature have deficiencies. In this study, these deficiencies were briefly demonstrated and then a new approach for fractional order derivative which was developed by Karci in 2013, will be given. After that, the relationships between classical derivative and this new approach will be illustrated and then some properties of this new definition will be given. There must be a relationship between results of derivative process and complex numbers since the result of derivative is a vectorial magnitude and complex numbers are also vectorial magnitudes. This relationship will be given in detail in this study.